A method for evaluating contact stress distribution of rock mass structural plane

Abstract

The application discloses a method for evaluating contact stress distribution of rock mass structure surface, comprising the following steps: firstly, performing preliminary point cloud registration on the upper disc point cloud and the lower disc point cloud of the structure surface, then dividing the coordinate system into zones, taking the mean value as the representative value of the horizontal, vertical and longitudinal directions of the grid, simplifying the upper disc point cloud and the lower disc point cloud, and performing accurate point cloud registration again; obtaining the complex topography of the upper disc point cloud and the lower disc point cloud after accurate point cloud registration; determining the position and geometric characteristics of the micro asperity according to the elevation matrix distribution; determining the stiffness of the micro asperity and the structure surface matrix and the series stiffness of the two according to the mechanical parameters of the structure surface; determining the contact deformation of the micro asperity according to the balance equation, and obtaining the contact area caused by the micro asperity under the current stress state; obtaining the total contact stress of the micro asperity area, and traversing all the micro asperities to obtain the contact stress distribution of the structure surface. The application can estimate the size of the contact stress of the rock mass structure surface.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of stress measurement between rock mass structural planes, in particular to a method for evaluating contact stress distribution of rock mass structural planes. BACKGROUND

[0002] Structural planes exist widely in natural rock mass, and the contact state of the structural planes has a decisive influence on the stability of the rock mass structure, the seepage characteristics and the propagation characteristics of stress waves. The size of the contact stress on the structural plane is crucial to reveal the seepage and sliding failure law of the rock mass and the internal mechanical mechanism. Moreover, the evaluation of the contact stress of the structural plane is of great significance for the early warning and prediction of rock mass sliding disasters, such as rock landslide and structural plane sliding rock burst.

[0003] In the past research, scholars have made detailed research on the normal constitutive of rock mass structural plane, from empirical constitutive model to statistical constitutive model, but there is no detailed research and discussion on the stress of different contact areas of the structural plane. Under the action of normal stress, the real contact area between the structural planes only accounts for a small part of the nominal contact area of the structural plane, and there is a great difference between the real contact stress in the contact area and the nominal average contact stress of the structural plane. The real contact stress in the contact area of the structural plane is the direct cause of the damage of the microconvex body in the process of compression or shear sliding of the structural plane, and therefore the evaluation of the real contact stress on the structural plane is the basis for predicting the compression or shear behavior of the structural plane. Therefore, the calculation of the real contact stress of the contact area of the rock mass structural plane is of great significance for predicting the mechanical behavior of the structural plane and predicting and warning the structural plane disaster.

[0004] The prior art, the invention patent with publication number CN106682347A, a non-continuous deformation analysis method based on random strength of rock mass structural plane, generates random strength for each structural plane in the rock mass, and performs non-continuous deformation analysis simulation based on the random strength of each structural plane. This strength parameter value method is closer to the actual situation of the rock mass, and the calculation and analysis results are more accurate and true. SUMMARY

[0005] The technical problem to be solved by the present application is to estimate the size of the contact stress of the rock mass structural plane.

[0006] To solve the above technical problems, the present application provides the following technical scheme:

[0007] A method for evaluating the contact stress distribution of rock mass structural planes, comprising:

[0008] S100, the upper disc point cloud and the lower disc point cloud of the structural plane are preliminarily registered;

[0009] S200, partitioning the upper disc point cloud and the lower disc point cloud after the preliminary point cloud registration on the coordinate system, taking the mean value as the representative value of the grid in the horizontal, vertical and longitudinal directions of the coordinate system, simplifying the upper disc point cloud and the lower disc point cloud, and performing accurate point cloud registration on the simplified upper disc point cloud and the lower disc point cloud again;

[0010] S300, obtaining the complex topography of the upper disc point cloud and the lower disc point cloud after accurate point cloud registration; and determining the position and geometric characteristics of the microconvex body according to the elevation matrix distribution;

[0011] S400, determining the stiffness of the microconvex body and the structure surface matrix according to the mechanical parameters of the structure surface, and the series stiffness of the two;

[0012] S500, determining the contact deformation of the microconvex body according to the balance equation;

[0013] S600, obtaining the contact area caused by the microconvex body under the current stress state according to the contact deformation of the microconvex body;

[0014] S700, obtaining the total contact stress of the microconvex body region, and traversing all microconvex bodies to obtain the contact stress distribution of the structure surface.

[0015] Advantages: through the microconvex body characteristics on the structure surface topography, the microconvex body is taken as the medium of contact, the specific position of the microconvex body is identified, the contact stress thereof is calculated according to the geometric characteristics, and after traversing all the contacted microconvex bodies, the contact stress of different contact areas on the rock mass structure surface can be obtained, and a cloud chart can be drawn to query the contact stress of the region according to the position of the microconvex body.

[0016] In an embodiment of the present application, step S200 comprises: first, dividing the upper disc point cloud and the lower disc point cloud after the preliminary point cloud registration into grids in the horizontal and longitudinal directions of the coordinate system, and taking the mean value as the representative value of the grid in the horizontal and longitudinal directions; then, taking the vertical direction coordinates in each grid region as the elevation coordinates of the grid region; and finally, obtaining the simplified upper disc point cloud and the lower disc point cloud.

[0017] In an embodiment of the present application, the division basis for dividing the grids in the horizontal and longitudinal directions of the coordinate system is obtained through the following formula:

[0018] cell(ii,jj)={x,y,z|0.5ii≤x≤0.5(ii+1),0.5jj≤y≤0.5(jj+1)};

[0019] In the formula, x, y and z respectively represent the coordinates of the point cloud in the horizontal, vertical and longitudinal directions of the coordinate system, and cell(ii,jj) represents the name and position of the grid region where the point cloud is located;

[0020] The elevation coordinates are obtained through the following formula:

[0021]

[0022] wherein z'(ii,jj) represents the elevation coordinate of the point cloud in the grid area, N c (ii,jj) represents the number of point clouds in the grid area, and z' represents the vertical coordinate of all point clouds in the grid area.

[0023] In an embodiment of the present application, step S300 comprises:

[0024] S310, combining the top disc point cloud and the bottom disc point cloud after the registration of the accurate point cloud to obtain a composite topography.

[0025] S320, judging whether the elements in the elevation matrix satisfy a judgment rule, and if the judgment rule is satisfied, determining the region topography at the corresponding position as a microconvex.

[0026] S330, fitting the vertex coordinates of the microconvex selected in step S320 and the coordinates of the four adjacent points in the orthogonal direction of the fixed point coordinates into a sphere through the least square method, and taking the radius of the sphere as the radius of curvature of the microconvex.

[0027] In an embodiment of the present application, the composite topography is obtained through the following formula:

[0028] comb(x,y)=z u (x,y)+z l (x,y);

[0029] wherein comb(x,y) represents the composite topography, comb represents the elevation matrix after the registration, z u represents the top disc point cloud after the registration of the accurate point cloud, z l represents the bottom disc point cloud after the registration of the accurate point cloud, and x and y respectively represent the coordinates of the point cloud in the horizontal, vertical and elevation directions of the coordinate system.

[0030] The judgment rule is obtained through the following formula:

[0031] comb(ii,jj)>max{comb(ii-1,jj),comb(ii+1,jj),comb(ii,jj+1),comb(ii,jj-1)};

[0032] In the formula, max represents maximum value; comb represents the combined elevation matrix, (ii,jj) represents the position of the elevation matrix; comb (ii-1,jj), comb (ii+1,jj), comb (ii,jj+1), comb (ii,jj-1) represent the elevations of the four adjacent points in the orthogonal direction of the combined elevation matrix.

[0033] In an embodiment of the present application, step S400 comprises the following steps:

[0034] S410, according to the Hertz micro-asperity contact theory, the stiffness of the single micro-asperity when it is elastically deformed is obtained;

[0035] S420, according to the elastic theory, the maximum contact pressure at the center of the micro-asperity when the micro-asperity is subjected to a load, and the settlement of the part of the micro-asperity and the structure surface matrix in the contact area are obtained;

[0036] S430, the stiffness of the structure surface matrix is obtained according to the settlement.

[0037] In an embodiment of the present application, the Hertz micro-asperity contact theory is obtained by the following formula:

[0038]

[0039] In the formula, f an represents the pressure borne by the nth micro-asperity, E represents the elastic modulus of the rock mass, ρ n represents the radius of curvature of the nth micro-asperity in the composite topography, δ an represents the deformation of the nth micro-asperity in the composite topography;

[0040] The stiffness of the single micro-asperity when it is elastically deformed is obtained by the following formula:

[0041]

[0042] In the formula, k an represents the stiffness of the single micro-asperity when it is elastically deformed;

[0043] The maximum contact pressure is obtained by the following formula:

[0044]

[0045] In the formula, P0 represents the maximum contact pressure, F N represents the external load, π represents the circular constant, r b represents the contact radius of the micro-asperity and the matrix;

[0046] The settlement in the contact area is obtained by the following formula:

[0047]

[0048] wherein U z (r) represents the settlement of the contact zone, E * represents the equivalent elastic modulus of the upper and lower disc contact of the structural surface, r represents the contact range of the micro-convex body and the structural surface matrix;

[0049] The stiffness of the structural surface matrix is obtained by the following formula:

[0050]

[0051] wherein k bn represents the stiffness of the structural surface matrix, δ bn represents the deformation of the structural surface matrix; U z (0) represents the settlement of the contact zone when the contact range of the micro-convex body and the structural surface matrix is 0;

[0052] The series stiffness of the micro-convex body and the structural surface matrix is obtained by the following formula:

[0053]

[0054] wherein k n represents the series stiffness, k an represents the stiffness of the nth micro-convex body.

[0055] In an embodiment of the present application, in step S500, the contact deformation of the micro-convex body is obtained by the following formula:

[0056]

[0057] wherein f(δ n ) represents the contact deformation of the micro-convex body, δ n represents the total deformation, ρ n represents the radius of curvature of the micro-convex body of the composite topography, r b represents the contact radius of the micro-convex body and the structural surface matrix.

[0058] In an embodiment of the present application, in step S600, the contact area caused by the micro-convex body under the current stress state is obtained by the following formula:

[0059] A n = πρ n δ an = πρ n (δ n - δ bn );

[0060] wherein: An represents the contact area caused by the micro asperity, π represents the circular constant, ρ n represents the radius of curvature of the micro asperity of the composite morphology, δ an represents the deformation of the n-th micro asperity on the composite morphology, δ n represents the total deformation, δ bn represents the deformation amount of the structural surface matrix.

[0061] In an embodiment of the present application, in step S700, the total contact stress of the micro asperity region is obtained by the following formula:

[0062]

[0063] In the formula, σ n represents the total contact stress of the n-th micro asperity region, A n represents the contact area of the micro asperity region, δ an represents the deformation of the n-th micro asperity on the composite morphology, π represents the circular constant, f(δ an ) represents the contact force generated by the deformation of the n-th micro asperity on the composite morphology, ρ n represents the radius of curvature of the micro asperity of the composite morphology; π represents the circular constant, ρ n represents the radius of curvature of the micro asperity of the composite morphology, E * represents the equivalent elastic modulus of the contact between the upper and lower plates on the structural surface.

[0064] Compared with the prior art, the present application has the following beneficial effects:

[0065] (1) The present application divides the upper plate point cloud and the lower plate point cloud in the coordinate system and calculates the normal contact stress of the structural surface. The micro asperity morphology on the coordinate is more accurate, and the geometric parameters obtained when calculating the micro asperity geometric characteristics are more accurate.

[0066] (2) The present application performs two times of point cloud registration, and the contact radius of the micro asperity and the structural surface matrix is considered in the calculation process, so that the convergence effect of the micro asperity morphology is better.

[0067] (3) The present application has a rigorous mathematical mechanics derivation process, can better combine with the actual engineering in the contact stress prediction, and predict the area with larger stress generated when the structural surface slips.

[0068] (4) The calculation process of the present application is easy to combine with the programming program, and a specific implementation process is generated. The present application is combined with the engineering practice, and is easy to form a system integrating information collection, prediction and protection means.

[0069] (5) The present invention can set different calculation precision according to different computing capabilities. For example, it can disregard the deformation of the structural surface substrate or introduce friction parameters. The specific precision can be set according to the actual engineering precision requirements to improve work efficiency. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating a method for evaluating the surface contact stress distribution of rock mass according to an embodiment of the present invention.

[0071] Figure 2 This is a schematic diagram of the upper and lower disk cloud of the structural surface in an embodiment of the present invention.

[0072] Figure 3 This is a schematic diagram of the composite morphology in an embodiment of the present invention.

[0073] Figure 4 This is a schematic diagram of the contact between the micro-protrusion and its neighboring area in an embodiment of the present invention. Detailed Implementation

[0074] To facilitate understanding of the technical solution of the present invention by those skilled in the art, the technical solution of the present invention will now be further described in conjunction with the accompanying drawings.

[0075] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0076] Please refer to Figure 1 As shown, the present invention provides a method for evaluating the contact stress distribution at the structural surfaces of rock masses, comprising the following steps:

[0077] S100 performs preliminary point cloud registration on the upper and lower disk point clouds of the structural surface.

[0078] Please see Figure 1 and Figure 2 As shown, in one embodiment of the present invention, in step S100, the point cloud acquired by the 3D scanner is as follows: Figure 2 As shown, point cloud processing software such as CloudCompare or Geomagic Studio is used for denoising and encapsulation to align the upper and lower disk point clouds on the structural surface. The ICP (Iterative Closest Point) registration method is used iteratively until the error target is less than 0.001. Specifically, the process includes the following steps:

[0079] S110, set the reference point cloud and the test point cloud, and obtain a new point cloud coordinate matrix of the reference point cloud and the test point cloud after rigid body translation along the centroid of the point cloud.

[0080] The new point cloud coordinate matrix of the reference point cloud and the test point cloud is obtained by the following formula:

[0081]

[0082]

[0083] In the formula, P' represents the new point cloud coordinate matrix of the test point cloud after translation, P represents the test point cloud, p" represents the three-dimensional coordinates of the test point cloud, A represents the reference point cloud, A' represents the new point cloud coordinate matrix of the reference point cloud after translation, a' represents the three-dimensional coordinates of the reference point cloud, N represents the number of point clouds, and i = 1, 2, 3,..., N.

[0084] S120, obtain an intermediate variable composed of the new point cloud coordinate matrix of the reference point cloud and the test point cloud, and perform singular value decomposition on the intermediate variable.

[0085] The singular value decomposition on the intermediate variable is performed by the following formula:

[0086]

[0087] In the formula, W represents the intermediate variable, T represents the matrix symbol, U and V represent the singular vectors of the intermediate variable, and S represents the characteristic vector composed of the singular values of the intermediate variable.

[0088] S130, obtain a rotation matrix of the point cloud rigid body transformation according to the singular vectors of the intermediate variable, and obtain a translation matrix of the point cloud rigid body transformation according to the rotation matrix.

[0089] The rotation matrix and the translation matrix of the point cloud rigid body transformation are obtained by the following formula:

[0090] R = U * V T ;

[0091]

[0092] In the formula, R represents the rotation matrix of the point cloud rigid body transformation, T0 represents the translation matrix of the point cloud rigid body transformation, a i represents the coordinate vector of the reference point cloud, p i represents the coordinate vector of the test point cloud

[0093] S140, use the change matrix to preliminarily register the reference point cloud and the test point cloud in the same coordinate system.

[0094] wherein the change matrix is a rotation matrix and a translation matrix of the point cloud rigid body transformation, and the error objective function of the preliminary point cloud registration is:

[0095]

[0096] wherein f(R, T0) represents the error objective function of the preliminary point cloud registration.

[0097] S200, the upper disc point cloud and the lower disc point cloud after the preliminary point cloud registration are divided into grids in the coordinate system, the mean values of the grids in the horizontal and vertical directions of the coordinate system are taken as the representative values of the grids, the upper disc point cloud and the lower disc point cloud are simplified, and the simplified upper disc point cloud and the simplified lower disc point cloud are subjected to accurate point cloud registration again.

[0098] Referring to FIGS. 1 and 2, Figure 1 and Figure 2 In an embodiment of the present application, step S200 includes: first, dividing the upper disc point cloud and the lower disc point cloud after the preliminary point cloud registration into grids in the horizontal and vertical directions of the coordinate system, and taking the mean values of the grids as the representative values of the grids in the horizontal and vertical directions. Then, taking the mean values of the vertical direction coordinates in each grid region as the elevation coordinates of the grid region. Finally, obtaining the simplified upper disc point cloud and the simplified lower disc point cloud.

[0099] Specifically, the division basis for dividing the grids in the horizontal and vertical directions of the coordinate system is obtained by the following formula:

[0100] cell(ii,jj)={x,y,z|0.5ii≤x≤0.5(ii+1),0.5jj≤y≤0.5(jj+1)};

[0101] wherein x, y and z respectively represent the coordinates of the point cloud in the horizontal, vertical and vertical directions of the coordinate system, and cell(ii,jj) represents the name and position of the grid region in which the point cloud is located. That is, in the embodiment, the upper disc point cloud and the lower disc point cloud after the preliminary point cloud registration are divided into grids at intervals of 0.5 mm in the horizontal and vertical coordinates.

[0102] The elevation coordinates are obtained by the following formula:

[0103]

[0104] wherein z'(ii,jj) represents the elevation coordinates of the point cloud in the grid region, N c (ii,jj) represents the number of point clouds in the grid region, and z' represents the vertical coordinates of all point clouds in the grid region, in mm. Wherein ii, jj ∈ [1, 200] and are integers.

[0105] Two point clouds after simplification are obtained through this step, and ICP registration is performed once again, so that the kiss state is quickly and accurately achieved.

[0106] S300, obtain the compound topography of the upper disc point cloud and the lower disc point cloud after accurate point cloud registration; and determine the position and geometric characteristics of the microconvex body according to the elevation matrix distribution.

[0107] Referring to FIGS. 1 to 3, Figure 1 and Figure 3 in an embodiment of the present application, step S300 includes the following steps:

[0108] S310, combine the topography of the upper disc point cloud and the lower disc point cloud after accurate point cloud registration to obtain the compound topography.

[0109] The compound topography is obtained by the following formula:

[0110] comb(x,y)=z u (x,y)+z l (x,y);

[0111] In the formula, comb(x,y) represents the compound topography, comb represents the compound elevation matrix, z u represents the upper disc point cloud after accurate point cloud registration, z l represents the lower disc point cloud after accurate point cloud registration, and x and y respectively represent the coordinates of the point cloud in the horizontal, vertical and longitudinal directions of the coordinate system.

[0112] S320, determine whether the elements in the elevation matrix satisfy a judgment rule, and if the judgment rule is satisfied, the region topography at the corresponding position is determined as a microconvex body.

[0113] The judgment rule is obtained by the following formula:

[0114] comb(ii,jj)>max{comb(ii-1,jj),comb(ii+1,jj),comb(ii,jj+1),comb(ii,jj-1)};

[0115] In the formula, max represents the maximum value; comb represents the compound elevation matrix, (ii,jj) represents the position of the elevation matrix, and comb(ii-1,jj), comb(ii+1,jj), comb(ii,jj+1), comb(ii,jj-1) represent the elevations of the four adjacent points of the compound elevation matrix in the orthogonal direction.

[0116] S330, fitting the coordinates of the vertex of the micro asperity and the coordinates of the four adjacent points in the orthogonal direction of the coordinates of the vertex into a sphere by least square method, and taking the radius of the sphere as the radius of curvature of the micro asperity.

[0117] S400, determining the stiffness of the micro asperity and the substrate of the structure surface according to the mechanical parameters of the structure surface, and the series stiffness of the two.

[0118] Please refer to Figure 1 and Figure 4 In an embodiment of the present application, step S400 comprises the following steps:

[0119] S410, obtaining the stiffness of the single micro asperity when the single micro asperity is elastically deformed according to the Hertz micro asperity contact theory.

[0120] The Hertz micro asperity contact theory is obtained by the following formula:

[0121]

[0122] In the formula, f an represents the pressure borne by the nth micro asperity, E represents the elastic modulus of the rock mass, and p n represents the radius of curvature of the nth micro asperity in the composite topography, and δ an represents the deformation of the nth micro asperity in the composite topography.

[0123] The stiffness of the single micro asperity when the single micro asperity is elastically deformed is obtained by the following formula:

[0124]

[0125] In the formula, k an represents the stiffness of the single micro asperity when the single micro asperity is elastically deformed.

[0126] S420, obtaining the maximum contact pressure at the center of the micro asperity when the micro asperity is subjected to a load, and the settlement of the part of the micro asperity and the substrate of the structure surface in the contact area according to the elastic theory.

[0127] The maximum contact pressure is obtained by the following formula:

[0128]

[0129] In the formula, P0 represents the maximum contact pressure, F N represents the external load, π represents the circular constant, and r b represents the contact radius of the micro asperity and the substrate of the structure surface.

[0130] In the formula, p In the formula, pn represents the radius of curvature of the nth asperity in the composite topography, h n represents the height of the nth asperity in the composite topography, i.e. h n represents the elevation of the composite topography at the position of the corresponding asperity.

[0131] The settlement in the contact zone is obtained by the following equation:

[0132]

[0133] wherein U z (r) represents the settlement in the contact zone, E * represents the equivalent elastic modulus of the upper and lower plates of the structural plane, r represents the contact range of the asperity and the substrate of the structural plane; r b represents the contact radius of the asperity and the substrate. Wherein wherein v represents the Poisson's ratio of the material, and is a constant.

[0134] S430, obtaining the stiffness of the substrate of the structural plane according to the settlement.

[0135] wherein the stiffness of the substrate of the structural plane is obtained by the following equation:

[0136]

[0137] wherein k bn represents the stiffness of the substrate of the structural plane, δ bn represents the deformation of the substrate of the structural plane, U z (0) represents the settlement of the contact zone when the contact range of the asperity and the substrate of the structural plane is 0.

[0138] The series stiffness of the asperity and the substrate of the structural plane is obtained by the following equation:

[0139]

[0140] wherein k n represents the series stiffness, k an represents the stiffness of the nth asperity.

[0141] S500, determining the contact deformation of the asperity according to the equilibrium equation.

[0142] Please refer to Figure 1 and Figure 4 In an embodiment of the present application, in step S500, according to the fact that the size of the interaction force is equal, it is obtained that:

[0143] k an δ an =kbn δ bn =k bn (δ n -δ an );

[0144] In the formula, k an Let δ represent the stiffness of the nth micro-convexity. an Let k represent the deformation of the nth micro-protrusion in the composite morphology. bn The stiffness of the structural plane matrix, δ bn The deformation of the structural surface matrix is ​​expressed as δ. n This is represented as the total deformation.

[0145] Simplifying the above equation, we get:

[0146]

[0147] In the formula, ρ n Let rb represent the radius of curvature of the nth micro-protrusion in the composite morphology, and let rb represent the contact radius between the micro-protrusion and the structural surface matrix.

[0148] The deformation of the micro-convexity is related to the total deformation, i.e., δ an =f(δ), which can be solved using the fixed-point iteration method. The contact deformation of the micro-convex body is then obtained by the following formula:

[0149]

[0150] In the formula, f(δ) n ) represents the contact deformation of the micro-convexity, δ n Represented as total deformation, ρ n Let r be the radius of curvature of the micro-convexity with a composite morphology. b This represents the contact radius between the micro-protrusion and the structural surface substrate.

[0151] S600, based on the contact deformation of the micro-protrusion, obtain the contact area caused by the micro-protrusion under the current stress state.

[0152] Please see Figure 1 and Figure 4 As shown, in one embodiment of the present invention, in step S600, the contact area caused by the micro-protrusion under the current stress state is obtained by the following formula:

[0153] A n =πρ n δ an =πρ n (δ n -δ bn );

[0154] In the formula: A nrepresents the contact area caused by the micro asperity, represents the circular constant, and f (δ n represents the radius of curvature of the micro asperity of the composite topography, and δ an represents the deformation of the n-th micro asperity on the composite topography, and δ n represents the total deformation, and δ bn represents the deformation amount of the structural surface matrix.

[0155] S700, the total contact stress of the micro asperity region is obtained, and all the micro asperities are traversed to obtain the contact stress distribution of the structural surface.

[0156] Please refer to Figure 1 and Figure 4 In an embodiment of the present application, the total contact stress of the micro asperity region in step S700 is obtained by the following formula:

[0157]

[0158] In the formula, σ n represents the total contact stress of the n-th micro asperity region, A n represents the contact area of the micro asperity region, and δ an represents the deformation of the n-th micro asperity on the composite topography, represents the circular constant, and f (δ an ) represents the contact force generated by the deformation of the n-th micro asperity on the composite topography, and ρ n represents the radius of curvature of the micro asperity of the composite topography; represents the circular constant, and ρ n represents the radius of curvature of the micro asperity of the composite topography, and E * represents the equivalent elastic modulus of the upper and lower disc contact on the structural surface.

[0159] When all the micro asperities are traversed, the calculated micro asperity returns a specific stress value, and the cloud chart can be drawn to obtain the contact stress distribution of the rock mass structural surface. For example, the contourf function of matlab can be used, the horizontal and vertical coordinates are the position coordinates of the micro asperity, and the content is the contact stress size.

[0160] It is obvious to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application, and any reference signs in the claims should not be regarded as limiting the claims involved.

[0161] The above-described embodiments only represent the implementation of the application, the protection scope of the application is not limited to the above-described embodiments, and for those skilled in the art, several modifications and improvements can be made without departing from the concept of the application, and these all belong to the protection scope of the application.

Claims

1. A method of assessing contact stress distribution of structural planes of a rock mass, characterized by, The method comprises the following steps: S100, performing preliminary point cloud registration on the upper disc point cloud and the lower disc point cloud of the rock mass structural surface; S200, dividing the upper disc point cloud and the lower disc point cloud subjected to the preliminary point cloud registration into zones in a coordinate system, taking the mean values as the representative values of the grids in the horizontal, vertical and longitudinal directions of the coordinate system, simplifying the upper disc point cloud and the lower disc point cloud, and performing accurate point cloud registration on the simplified upper disc point cloud and the lower disc point cloud again; S300, obtaining the compound topography of the upper disc point cloud and the lower disc point cloud subjected to the accurate point cloud registration; and determining the position and geometric characteristics of the micro asperities according to the elevation matrix distribution; S400, determining the stiffness of the micro asperities and the structural surface matrix and the series stiffness of the two according to the mechanical parameters of the structural surface, comprising: S410, obtaining the stiffness of a single micro asperity subjected to elastic deformation according to the Hertz micro asperity contact theory; S420, obtaining the maximum contact pressure at the center of the micro asperity and the settlement of the part of the micro asperity and the structural surface matrix in the contact area when the micro asperity is subjected to a load according to the elastic theory; S430, obtaining the stiffness of the structural surface matrix according to the settlement; S500, determining the contact deformation of the micro asperity according to the balance equation and obtaining the contact deformation by the following formula: ； wherein contact deformation of the micro asperity, total deformation, radius of curvature of the micro asperity represented as a compound topography, contact radius of the micro asperity with the substrate of the structure surface; S600, obtaining the contact area caused by the micro asperity under the current stress state according to the contact deformation of the micro asperity; S700, obtaining the total contact stress of the micro asperity region and obtaining the contact stress distribution of the structural surface by traversing all the micro asperities.

2. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 1, characterized in that, Step S200 comprises: first, dividing the upper disc point cloud and the lower disc point cloud subjected to the preliminary point cloud registration into grids in the horizontal and longitudinal directions of the coordinate system, and taking the mean values as the representative values of the grids in the horizontal and longitudinal directions; then, taking the vertical direction coordinates in each grid region as the elevation coordinates of the grid region; and finally, obtaining the simplified upper disc point cloud and the lower disc point cloud.

3. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 2, characterised in that, The division basis for dividing the grids in the horizontal and longitudinal directions of the coordinate system is obtained by the following formula: ； In the formula, x, y and z respectively represent the coordinates of the point cloud in the horizontal, vertical and longitudinal directions of the coordinate system, represent the name and location of the square region in which the point cloud is located; The elevation coordinates are obtained by the following formula: ； wherein is represented as the elevation coordinate of the point cloud within the grid area, is represented as the number of point clouds within the grid area point cloud, is represented as the vertical coordinate of all point clouds within the grid area.

4. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 3, characterized in that, Step S300 comprises: S310, combining the topography of the upper disc point cloud and the lower disc point cloud subjected to the accurate point cloud registration to obtain the compound topography; S320, judging whether the elements in the elevation matrix satisfy the judgment rule, and if the judgment rule is satisfied, determining the region topography at the corresponding position as a micro asperity; S330, fitting a sphere by the least square method through the vertex coordinates of the micro asperity screened out in step S320 and the coordinates of the adjacent four points in the orthogonal direction of the vertex coordinates, and taking the radius of the sphere as the radius of curvature of the micro asperity.

5. The method of assessing contact stress distribution of a rock mass discontinuity of claim 4, wherein, The compound topography is obtained by the following formula: ； In the formula, is expressed as a composite morphology, is expressed as an upper disc point cloud after accurate point cloud registration, is expressed as a lower disc point cloud after accurate point cloud registration, x, y respectively represent the coordinates of the point cloud in the horizontal, vertical and longitudinal directions of the coordinate system. The judgment rule is obtained by the following formula: ； In the formula, max represents a maximum value; represents the elevation matrix after the composition, represents the position of the elevation matrix; represents the elevations of the four points adjacent to the elevation matrix after the composition in the orthogonal direction.

6. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 1, characterized in that, The Hertz micro asperity contact theory is obtained by the following formula: ； wherein P represents the pressure on the n th asperity, E E represents the elastic modulus of the rock mass, R represents the radius of curvature of the n th asperity in the composite topography, δ represents the deformation of the n th asperity in the composite topography; The stiffness of a single micro asperity subjected to elastic deformation is obtained by the following formula: ； In the formula, represents the stiffness when a single microconvexity is elastically deformed. The maximum contact pressure is obtained by the following formula: ； wherein expressed as maximum contact pressure, expressed as external load, π as the circle constant, expressed as the contact radius of the microprotrusions with the substrate; The settlement in the contact area is obtained by the following formula: ； wherein is the contact area of the asperity, is the equivalent elastic modulus of the contact between the upper and lower plates of the structural plane, r is the contact area of the asperity, The stiffness of the structural surface matrix is obtained by the following formula: ； wherein the rigidity of the structure surface base, the deformation of the structure surface base; the settlement of the contact area when the contact range of the micro-convex with the structure surface base is 0. The series stiffness of the micro asperity and the structural surface matrix is obtained by the following formula: ； wherein is expressed as the stiffness of the series, is expressed as the stiffness of the series, n is expressed as the stiffness of the series.

7. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 1, characterized in that, In step S600, the contact area caused by the micro asperity under the current stress state is obtained by the following formula: ； In the formulae: represents the contact area caused by the micro-asperity, and π represents the circular constant, represents the radius of curvature of the micro-asperity of the composite topography, represents the deformation of the first n micro-asperity on the composite topography, represents the total deformation, represents the deformation amount of the structure surface matrix.

8. The method of assessing contact stress distribution of structural planes of a rock mass according to claim 1, characterized in that, In step S700, the total contact stress of the micro asperity region is obtained by the following formula: ； wherein total contact stress of the nth asperity region, n total contact stress of the nth asperity region, contact area of the nth asperity region, deformation of the nth asperity on the composite topography, π denotes the circular constant, n contact force of the nth asperity on the composite topography due to the deformation, contact force of the nth asperity on the composite topography due to the deformation, n radius of curvature of the asperities of the composite topography; π denotes the circular constant, radius of curvature of the asperities of the composite topography, radius of curvature of the asperities of the composite topography, E equivalent elastic modulus of the contact between the upper and lower plates on the structural surface.

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